Played the game a bit more, and it looks like the main problem I was having was the boss's attacks dealing far too much damage. Mistime a parry, and you can potentially lose half your health.
In the first few attempts that made it to phase 3, I died before I even really knew what was going on.
Though I do finally understand what this game us going for. Sticking close to the boss is legitimately safer than keeping your distance, and lets you take her down faster, too.
Perhaps you could add I-frames, but only every 20ish% of your life bar like in Gunstar Heroes, just so the bosses can't wipe out half your health with one attack.
Edit: Corrected spelling, added anecdote about dying to Phase 3 before I could get my bearings, added suggestion for Gunstar Heroes-style I-frames